The invention relates to a network of track-bound vehicles which cover prescribed routes. Optimum control of the vehicles requires taking into account a plurality of boundary conditions, for example that in a network intensively covered by vehicles, the passengers typically do not arrive at the respective stopping places at the envisaged departure times of the vehicles, but take the next available vehicle in the desired direction.
Moreover, high-frequency networks are subject to random effects in many regards. If, because of the fluctuations in the influx of the passengers, or because of delays to the vehicles there are more passengers than usual standing at the stopping place, the stopping time increases correspondingly due to the lengthened boarding process, and the spacing from the predecessor train increases. Because of this small delay, however, on average, more passengers than usual board at the next stopping place, and the delay of the train lengthens further.
It is therefore a case of a reinforcing random feedback which in the final analysis has the effect that an overcrowded, late vehicle is running immediately in front of a sparsely occupied vehicle.
Furthermore, the journey times of the vehicles between the stopping places are likewise subject to random fluctuations, for example caused by deviations from normal operation inside the vehicle, on the route or in any signalling engineering present.
Relatively serious disturbances occurring at some points and causing delays to the vehicles can also occur during the stops at the stopping places.
It has been found that many random small or individual relatively serious disturbances have the effect that lacking control of the vehicles the delays grow exponentially given an average passenger density, which can lead to substantial problems.
A method for determining a minimum of a multi-dimensional function is known, for example, as a method of steepest descent. An efficient method for determining the gradient of a multidimensional function is known as the back-propagation algorithm (D. Rumelhart et al., Parallel Distributed Processing, Bradford Books, MIT Press, Cambridge, Mass., ISBN 0-262-68053-X, pages 381 to 362, 1987).
Furthermore, heuristic methods are known for controlling track-bound vehicles (S. Araya, Traffic Dynamics of Automated Transit Systems with Pre-established Schedules, IEEE Transactions On Systems, Man and Cybernetics, Vol. 14, No. 4, pages 677 to 687, July/August 1984; J. Bustinduy et al., Timetable and Headway Control, Computers in Railway Operations, Computational Mechanics Publication, Southhampton, pages 317 to 336, 1987).
Also known is a deterministic model for controlling track-bound vehicles (V. Van Breusegem et al., Traffic Modelling and State Feedback Control for Metro Lines, IEEE Transactions on Automatic Control, Vol. 36, No. 7, pages 770 to 784, July 1991).
The methods which use local heuristics to control track-bound vehicles are subject to some limitations and thus harbour some disadvantages. These methods are all based on a local approach, that is to say the control instruction to a vehicle is determined only on the basis of information relating to the location of direct predecessor and successor trains. Information relating to more remote vehicles is not taken into account in controlling the vehicles. Furthermore, no actual optimum solution for controlling the vehicles is determined, since the methods are based exclusively on heuristic approaches. The applicability of these methods is, further, limited to simple route networks with only one line.
The deterministic method for controlling the track-bound vehicles also does not offer an optimum solution for controlling the vehicles, since insufficient account is taken of uncertainties such as, for example, irregular delays, determined by random effects, such as, for example, the delays in boarding and alighting processes, or random delays in the journey times of the vehicles between two stopping places.